I am looking for mathematical documentaries, both technical and non-technical. They should be "interesting" in that they present either actual mathematics, mathematicians or history of mathematics. I am in charge of nourishing our departmental math library (PUCV) and I would like to add this kind of material in order to attract undergraduates toward mathematics. For this reason, I am not looking for videos of conferences or seminar talks, but rather for introductory or "wide public" material.

"The Color of Math" is a rather poetic documentary by Katia Eremenko that will have its premiere at the Moscow Film Festival this upcoming Saturday, June 23, 2012. It features Cedric Villani, Anatoly Fomenko, Maxim Kontsevic, Jean-Michel Bismut, Aaditya V. Rangan (and myself).

Marcus du Sautoy's The Story of Maths is a total of four hours attempting to give an overview of the history of mathematics from ancient to modern time, spending 5-10 minutes each on the life and work of some of the most famous mathematicians. While one could quibble with some of the selections, the project is overall a fantastic production.

Something completely different, but I'm sure a lot of people here at MO would enjoy:

Beautiful young minds British documentary about International Mathematical Olympiad 2006 with focus on the UK team.

Hard problems American documentary about the same event with focus on the US team.

Documentaries contain analysis of that year's problems (although the focus is on the competition in general, team selection and contestants - which makes it more interesting to ex-contestants than to professional mathematicians or math enthusiasts).

The soundtrack is still in progress, so it's not yet fully available but Ester Dalvit made a very interesting movie about braids and knots. At the end it will be distributed under a Creative commons license.

A trailer and parts of the movie are available here. Up to now three (old versions of) chapters are available, explaining respectively through computer generated animations:

the group structure of the braid group

"combing" of braids and handle reduction (i.e. solutions to the world problem)

Here the synopsis from IMDB: "When France surrendered in 1940 and German soldiers showed up in the Vosgian village of Housseras, an unknown French foot soldier burned his papers and killed himself in a farmer's barn. Four years later he was identified as "soldat Doblin, Vincent". In fact, he was none other than the mathematician Wolfgang Doeblin, son of the famous German novelist Alfred Döblin ("Berlin Alexanderplatz") who was forced to flee Nazi Germany with his family in 1933. A French citizen since October 1936, Wolfgang Doeblin carried on his research into probability theory during his military service and even during the hardships of the "Phoney War" in the winter of 1939-40. In February 1940, four months before his death at the age of 25, he sent his most important manuscripts ("About the Kolmogoroff Equation") as a "sealed envelope" to the Academy of Science in Paris, where they were kept in safe custody for 60 years. Wolfgang Doeblin's short and dramatic life story, almost forgotten, was finally brought into the limelight when the "sealed envelope" was opened in May 2000. Far ahead of their time, his groundbreaking contributions to the theory of random processes place Wolfgang Doeblin among the major innovators of probability, the "mathematics of randomness". Mathematical models for evaluation of chances and risks went on to gain major importance in numerous domains of modern science, in everyday life and especially in contemporary financial mathematics."

The code-breaking work at Bletchley Park, which helped save Britain from Nazi Germany, qualifies as one of the greatest stories of World War II, and the misunderstood genius, Alan Turing, stands at the center of this tale. Perhaps no one understands Turing's role during this period -- and his larger impact on mathematics and computing -- like B. Jack Copeland. In this lecture, Copeland contends that Turing should be celebrated as the father of artificial intelligence.

In this one-off documentary, David
Malone looks at four brilliant
mathematicians – Georg Cantor, Ludwig
Boltzmann, Kurt Gödel and Alan Turing
– whose genius has profoundly affected
us, but which tragically drove them
insane and eventually led to them all
committing suicide.

Do we really want to encourage the view that mathematics is done by insane geniuses?
–
Steven GubkinJun 20 '12 at 1:19

15

Except for Gödel, it is grossly inaccurate to say that they became insane, even because of their genius. For Cantor and Boltzmann, this was because of the bad acception of their works, and for Turing, because of terribly stupid law.
–
BS.Jun 20 '12 at 9:17

1

It seems very likely that Boltzmann suffered from bipolar disorder. However, I agree with Steven that this Romantic trope of the "thin line between madness and genius" can be very tiresome indeed.
–
Todd Trimble♦Dec 16 '12 at 16:27

Science Lives, made by the Simons Foundation, has nine very long interviews that essentially amount to miniature documentaries about the lives of a number of 20th/21st century mathematicians and physicists.

I vote for 100年の難問はなぜ解けたのか
～天才数学者 失踪の謎 ("Why the difficult 100-year-old conjecture was proven- The mysterious disappearance of the genius mathematician"), about Grigory Perelman, Geometrization, and the proof of the Poincaré Conjecture, as the best mathematical documentary ever. It's non-technical, but it's really very well-made, and gives a good sense of what research mathematics is like, and why some people spend their lives searching for proofs of mathematical conjectures. The mathematics in it is mostly fairly solid. It inspired fashion design house Issey Miyake to design a fashion collection with Bill Thurston inspired by geometrization.

The Geometry Center (formerly of UMN, now apparently defunct) many years ago produced "Not Knot" (about hyperbolic space) and "Outside In" (about sphere eversion). There is apparently a more recent third one "The Shape of Space" I'm not familiar with. Apparently you can still order them here, although copies are now easily found on YouTube.

The only documentary about Grigori Perelman has recently got English subtitles. (Perelman is the guy who proved the Poincare conjecture and then refused a million dollar prize.) It is for laymen, and very dramatic.

Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.

Program Description

You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart. In this film, NOVA takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.

For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory. Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design. The documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire.
Aired August 24, 2011 on PBS

My friend watched this in University of Waterloo: BBC: Code Breakers Bletchley Parks lost Heroes
This is not about the Enigma Machine, which is probably the more well known example in code breaking. Instead, this is about the Lorenz cipher.
This is a relatively new movie (october 2011) that talked about how a maths student and an engineer combined to hack into Hitler's personal super-code machine, named the secret writer, and helped win WWII. Also of historical significance, the movie described the decryption machine as the first programmable computer.